Free Printable Quadratic Functions Test

1.

Standard form of a quadratic equation

a)

y=x²

b)

y=ax²+bx+c

c)

y=mx+b

d)

y=x

2.

The graph of a quadratic function is called a

a)

Parabola

b)

Vertex

c)

Axis of Symmetry

d)

Vertex Form

3.

A parabola is upside-down when a is:

a)

negative

b)

positive

c)

0

d)

infinite

4.

Which best describes the vertex of a parabola?

a)

Any point on the parabola.

b)

A point on the x-axis.

c)

The highest or lowest point of a parabola

d)

A point on the y-axis.

5.

Name the vertex

a)

(1,1)

b)

(0,0)

6.

What is the vertex?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

7.

What is the vertex?

a)

(5,2)

b)

(2,5)

c)

(-2,5)

d)

(-5,2)

8.

Does this graph have a maximum or minimum value?

a)

maximum

b)

minimum

c)

neither

d)

both

9.

Does this parabola have a minimum or maximum and what is its value?

a)

minimum: 2

b)

maximum: 2

c)

minimum: 5

d)

maximum: 5

10.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

symmetrical point for the vertex

11.

What is the equation for axis of symmetry?

a)

y = 3

b)

x = 3

c)

x = 5

d)

x = 1

12.

Name the Axis of Symmetry

a)

x = 1

b)

x = 0

13.

Is this a maximum or a minimum?

a)

max

b)

min

c)

cannot be determined

14.

Does this graph have maximum or minimum value?

a)

maximum

b)

minimum

c)

neither

d)

both

15.

What are the x-intercept(s) of this graph?

a)

-1 and -3

b)

-1 and 3

c)

1 and 3

d)

1 and -3

16.

What are the coordinates of the y-intercept?

a)

(-3, 0)

b)

(0, -3)

c)

(2, 1)

d)

y=-3

17.

What are the X-intercept(s) of this graph?

a)

-1 and -3

b)

1 and -3

c)

1 and 3

d)

-1 and 3

18.

What are the coordinates of the y-intercept?

a)

(-3, 0)

b)

(0, -3)

c)

(2, 1)

d)

y=-3

19.

What is the y-intercept of this graph?

a)

-6

b)

-2

c)

3

d)

5

20.

Use the picture to find the vertex and axis of symmetry.

a)

Vertex: (8, 3); axis of symmetry: y=3

b)

Vertex: (8, 3); axis of symmetry: x=3

c)

Vertex: (3, 8); axis of symmetry: y=3

d)

Vertex: (3, 8); axis of symmetry: x=3

21.

What is the vertex?

a)

(-2,0)

b)

(0,0)

c)

(0,-4)

d)

(2,0)

22.

Select the answer that has a, b, and c correctly labeled:

y=-x^2+2x-9

a)

a= 1, b= 2, c= -9

b)

a= 2, b= -1, c= 9

c)

a= -9, b= 2, c= -1

d)

a= -1, b= 2, c= -9

23.

What is the equation of the line of symmetry for this quadratic function?

a)

x = -3

b)

x= .5

c)

x = 4

d)

x = -12

24.

Which direction will this parabola open?

y=2x^2+8x-16

a)

upwards

b)

downwards

25.

What is the green dot on the parabola called?

a)

maximum

b)

minumum

c)

roots

d)

zeros

26.

What is the vertex of the quadratic function:
y = x² - 6x + 11?

a)

(3,2)

b)

(-3,-2)

c)

(-3,2)

d)

(3,-2)

27.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

none of these

28.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

29.

What is another name for the x-intercepts of a quadratic?

a)

y-intercepts

b)

zeros

c)

x-axis

d)

none of these

30.

Factor completely
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

31.

Factor completely
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

32.

Factor completely
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

33.

Identify the 'a' value: y = 16x² -8x -24

a)

16

b)

8

c)

-8

d)

-24

34.

Solve by factoring
x² + 13x + 12 = 0

a)

x = -12, -1

b)

x = 12, 1

c)

x = 13, 1

d)

x = -13, -1

35.

Factor: x² + 2x – 3

a)

(x - 2)(x + 1)

b)

(x + 1)(x - 3)

c)

(x + 2)(x - 1)

d)

(x - 1)(x + 3)

36.

Identify the 'b' value: y = 16x² -8x -24

a)

16

b)

-8

c)

8

d)

-24

37.

Does this graph have a maximum or minimum?

a)

Minimum

b)

Maximum

38.

What are the green dots called?

a)

axis of symmetry

b)

vertex

c)

parabola

d)

roots or x-intercepts

39.

What is the axis of symmetry of:y=2x²-4x+9

a)

x = 1

b)

x = -1

c)

x = -2

d)

x = 4

40.

What is the y-intercept of: y=7x²+2x -1

a)

(0, 1)

b)

(0, -1)

c)

(1, 0)

d)

(-1, 0)

41.

What is the y-intercept?
f(x) = -2x² + 4x - 6

a)

(0, 6)

b)

(0, -6)

c)

(6, 0)

d)

(-6, 0)

42.

What do we call the highest or lowest point of a quadratic?

a)

parabola

b)

vertex

c)

graph

d)

point

43.

What is the green dot on the parabola called?

a)

maximum

b)

minumum

c)

roots

d)

zeros

44.

The standard form of a quadratic function is

a)

y = ax² + bx + c

b)

a(x - h)² + k

c)

y - y₁= m(x - x₁)

d)

Ax + By = C

45.

Identify a, b, and c if y = +3x²+5x - 8

a)

a=3, b=5, c= - 8

b)

A=3, B=-8, C=5

c)

A=3x², B=5x, C=-8

d)

A=3x² , B=-8, C=5x

46.

Does this parabola have a maximum or minimum?

a)

Maximum

b)

Minimum

47.

What do we call the graph of a quadratic?

a)

line

b)

vertex

c)

equation

d)

parabola

48.

What is the y-intercept? $x^2-3x+9$

a)

(9, 0)

b)

(0, 9)

c)

(1, 0)

d)

(-3, 0)

e)

(0, -3)

49.

What is the axis of symmetry?
f(x) = x²- 8x + 15.

a)

x = -4

b)

x = 4

c)

y = 4

d)

y = -4

50.

What is the vertex?
f(x) = -x²- 4x + 12.

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

51.

In the function

y\ =\ 7x^2\ +8x\ -\ 10

,
the vertex is a ......

a)

minimum

b)

maximum

52.

Where is the axis of symmetry for this parabola?

a)

x = −1

b)

x = 0

c)

y = 3

d)

x = −3

53.

What is the axis of symmetry?
y = 3x²- 6x + 4

a)

x=1

b)

x=-6

c)

x=2

d)

x=-1

54.

Find the Vertex: y= -5x²-20x - 26

a)

(-2, -6)

b)

(2, 6)

c)

(6,2)

d)

(3, 6)

55.

The vertex of parabola y = - 2x² - 4x + 1 is

a)

(1, 3)

b)

(- 1, 3)

c)

(- 1, -5)

d)

(- 1, 5)

56.

A parabola has a vertex at (-3,2).
Where is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

57.

Which formula allows you to find the x-value of the vertex from a standard form equation?

a)

$x=-\frac{b}{2a}$

b)

$x=\frac{\left(p+q\right)}{2}$

c)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

d)

$x=h$

58.

The axis of symmetry for a vertical parabola always matches...

a)

the y-intercept

b)

the y-value of the vertex

c)

the x-value of the vertex

d)

the x-intercepts

59.

Find the vertex, AOS, and y-intercept for the following equation.

y=-4x^2+20x-22

Choose all below that apply.

a)

Vertex: $\left(\frac{5}{2},\ 3\right)$

b)

Vertex: $\left(-\frac{5}{2},\ -97\right)$

c)

AOS: $x\ =\ \frac{5}{2}$

d)

AOS: $x\ =\ -\frac{5}{2}$

e)

y-intercept: $\left(0,\ 3\right)$

60.

Identify a: f ( x ) = 3x² + 4x - 5

a)

3

b)

4

c)

5

d)

-5

61.

Describe the transformations of f(x) when compared to the parent function.
f(x)=x²+5

a)

horizontal shift right 5 units

b)

horizontal shift left 5 units

c)

vertical shift up 5 units

d)

vertical shift down 5 units

62.

Describe the transformations of f(x) when compared to the parent function.
f(x)=(x+7)²

a)

horizontal shift left 7 units

b)

horizontal shift right 7 units

c)

vertical shift up 7 units

d)

vertical shift down 7 units

63.

In the equation f(x)=5(x+3)²-10 what effect does the 5 do when compared to the parent function?

a)

Vertical stretch by a factor of 5

b)

Vertical shrink/compress by a factor of 5

c)

Reflect over x-axis

d)

Vertical shift up 5 units

64.

Which of the following describes the transformations done to the quadratic parent function of f(x) = x² to obtain g(x) = 2x² + 4 ?

a)

Vertical Stretch by a factor of 2 and vertical shift up 4 units

b)

Vertical Shrink/Compress by a factor 2 and vertical shift up 4

c)

Vertical Stretch by a factor of 2 and horizontal shift left 4 units

d)

Vertical Shrink/Compress by a factor of 2 and horizontal shift right 4 units

65.

If the blue is f(x)=x^2,the red must be

a)

g(x)=(x+3)²

b)

g(x)=(x-3)²

c)

g(x)=x²+3

d)

g(x)=x²-2

66.

Which of the following quadratic functions has the WIDEST graph?

a)

f(x)= -3x²

b)

h(x)= 2x²

c)

g(x)= ¼x²

d)

p(x)= 4x²

67.

Which of the following is the correct equation for the given graph?

a)

f(x) = (x - 2)² - 1

b)

f(x) = (x + 2)² - 1

c)

f(x) = -(x + 2)² - 1

d)

f(x) = -(x - 2)² - 1

68.

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

69.

A parabola has a vertex at (-3,2).
Where is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

70.

Does the graph of this equation open up or down?

f(x) = -(x + 3)² - 5

a)

up

b)

down

71.

What is Standard Form for Quadratic Equations?

(a)

72.

What is Vertex Form for Quadratic Equations?

(a)

73.

What does the a in Vertex Form tell you about the parabola in your graph?

a)

If the parabola is going Upward or Downward

b)

If the parabola is going left or right

74.

$y=\left(x-1\right)^2+3$

75.

$y=\left(x+3\right)^2-2$

76.

y = -2(x+1)²+3

77.

Determine the domain and range of the function

a)

Domain: All real numbers

Range: All real numbers

b)

Domain: x ≥ -4

Range: All real numbers

c)

Domain: All real numbers

Range: y ≥ -4

d)

Domain: -1 ≤ x ≤ 5

Range: y ≥ -4

78.

What is the domain and the range for the graph?

a)

Domain : -2 ≤ x ≤ 2
Range : 0 ≤ y ≤ 4

b)

Domain : 0 ≤ x ≤ 4
Range : -2 ≤ y ≤ 2

c)

Domain : All real #s
Range : y ≤ 4

d)

Domain : -2 ≤ x ≤ 2
Range : y ≤ 4

79.

What are the coordinates of the y-intercept?

a)

(-3, 0)

b)

(0, -3)

c)

(2, 1)

d)

y=-3

80.

What is another name for the x-intercepts and solutions of a quadratic?

a)

y-intercept

b)

Zeros

c)

x-axis

d)

They don't have another name

81.

Use the graph to determine the solutions.

a)

-1 and -3

b)

1 and -3

c)

1 and 3

d)

-1 and 3

82.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

83.

Use the picture to find the vertex and axis of symmetry

a)

Vertex (3,8) Axis x = 3

b)

Vertex (3,8) Axis y = 3

c)

Vertex (8,3) Axis x = 3

d)

Vertex (8,3) Axis y = 3

84.

Does this parabola have a minimum or maximum and what is its value?

a)

minimum: 2

b)

maximum: 2

c)

minimum: 5

d)

maximum: 5

85.

Quadratic equations take the shape of a _______ when graphed.

a)

parabola

b)

straight line

c)

snaked line

d)

elliptical

Quadratic Functions Test

Total questions: 85

Worksheet time: 3hrs 55mins

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